On the third logarithmic coefficient in some subclasses of close-to-convex functions
By Nak Eun Cho, B. Kowalczyk, Oh Sang Kwon, Adam Lecko, Young Jae Sim. RACSAM, 2020
55 citations recorded by the source corpus.
For analytic functions f in the unit disk D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document} normalized by f(0)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(0)=0$$\end{document} and f′(0)=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f'(0)=1$$\end{document} satisfying in D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {D}}$$\end{document} respectively the conditions Re{(1-z)f′(z)}>0,Re{(1-z2)f′(z)}>0,Re{(1-z+z2)f′(z)}>0,Re{(1-z)2f′(z)}>0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{Re}\,}}\{ (1-z)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z+z^2)f'(z) \}> 0,\ {{\,\mathrm{Re}\,}}\{ (1-z)^2f'(z) \} > 0,$$\end{document} the sharp upper bound of the third logarithmic coefficient in case when f′′(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f''(0)$$\end{document} is real was computed.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c078e95afaaccb301d4b5ac1810ebd96f2248899
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha (2021, background): “Logarithmic coefficients have recently attracted considerable interest (see [2, 3, 6, 10, 13, 20]).”